The Solution:
Given the diagram below:
Considering right-angled triangle ABC,
we can apply the Trigonometrical Ratio as below:
[tex]\begin{gathered} \tan 25^o=\frac{y}{87} \\ \text{Cross multiplying, we get} \\ y=87\tan 25^o\ldots eqn(1) \end{gathered}[/tex]
Similarly, considering right-angled triangle ABD,
we can apply the Trigonometrical Ratio as below:
[tex]\begin{gathered} \tan 40^o=\frac{x+y}{87} \\ \text{Cross multiplying, we get} \\ x+y=87\tan 40^o\ldots eqn(2) \end{gathered}[/tex]
Now, putting eqn(1) into eqn(2), we get
[tex]x+87\tan 25^o=87\tan 40^o[/tex]
Solving for x, we have
[tex]\begin{gathered} x=87\tan 40^o-87\tan 25^o \\ x=87(\tan 40^o-\tan 25^o) \end{gathered}[/tex][tex]x=87(0.8390996-0.4663077)=87\times0.37279=32.4329\approx32.43\text{ feet}[/tex]
Therefore, the correct answer is 32.43 feet.
